If a person baptized in the Catholic Church does not observe the correct form, they marry invalidly. However-- and this is a BIG however-- the form of Catholic marriage is the exchange of vows before a lawfully appointed minister of the Catholic Church. It is not the wedding mass, nor even the prescribed nuptial rite itself. It has everything to do with who is witnessing the marriage on behalf of the Church.
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An even bigger "however" is the fact that canon 1098 allows a couple to marry in front of non-appointed witnesses if it is foreseen that their pastor will not be available within a month. I believe that due to the crisis of the Church, canon 1098 applies more or less wholesale to Catholic marriages today, rendering many marriages which would otherwise be invalid, valid.